Question

Two bodies of masses 6 kg and 4 kg are moving along eastern and northern

directions with velocities 5ms–1 and 10ms–1 respectively. Find the magnitude​

Answer 1

Answer:ANSWER

Let east direction be x axis and north be y axis. Then, velocity of first body is v

1

​

=5im/s and that of body 2 will be v

2

​

=3jm/s. Since velocity of center of mass is given by

v

cm

​

=

m

1

​

+m

2

​

m

1

​

v

1

​

+m

2

​

v

2

​

​

=

4+5

4(5i)+5(3j)

​

=

9

20

​

i+

9

15

​

jm/s

Hence, magnitude of velocity is ∣v

cm

​

∣=

9

400+225

​

​

m/s=

9

25

​

m/s.

Explanation:

Answer 2

Given: Mass = 6kg, 4kg

          Velocity = 5m/s, 10m/s

To find: The magnitude of resultant velocity

Solution:

Let east direction be x-axis and north be y-axis.

Then, the velocity of the first body is v₁  = 5im/s and that of body 2 will be v₂  = 10jm/s.

Since the velocity of the center of mass is given by v cm = (m₁v₁  + m₂v₂)/(m₁+m₂)

= { 6(5i)+4(10)j) }/6+4

= 30/10i + 40/10j m/s

= 3i + 4j m/s

​     ​ Hence, the magnitude of velocity is ∣v| = $\sqrt{3^2 + 4^2$

= $\sqrt{9 + 16$ m/s

= 5 m/s

Therefore, the magnitude of the velocity = 5 m/s.

• The Centre of mass is the average position of all the parts of the system, weighted according to their masses.
• Velocity is the rate of change of displacement, and its magnitude is equal to the displacement divided by the time taken.
• Velocity is a vector quantity. It has both magnitude and direction.